The original original Rura Penthe was of course both. That is, Jules Verne had it as a hot place, probably somewhere in the Pacific, while Leo Tolstoy had it in deep Siberia.

Anybody know the etymology of the name?

But why would the Narada need to be in Klingon space in the first place?

To meet Spock?

Remember that when Nero emerged from the future, he was at a location where Robau's crew was concerned the Klingons were just 75,000 km away or something like that. Now, we don't have a specific reason to think that Nero and Spock would have emerged from the future at separate locations. If there were Klingons at the point of emergence in 2233, there might be a Klingon armada there in 2258 as well.

On the other hand, it was said in the 2258 emergence scene that Nero had predicted the location of Spock's appearance, not just the time. But Ayel might be speaking of fine-tuning: Nero might have calculated where exactly within the already known star system they would have to wait so that Spock could be grabbed mere seconds after reaching the 23rd century and before getting his bearings.

In that scene, Nero also made it clear that they had indeed been "waiting" for the past 25 years. Doesn't mean they couldn't have had hilarious adventures in the meantime. But Romulans would be long-lived and patient - and waiting might be the only thing this bunch would be capable of.